Hello, need help solving a problem.I know that it’ll take 20 min to fill the pond but not how to write the equation or graph
Answers
It is given that the pond already has 600 liters of water and that it is filled at a rate of 30 liters per minute.
It is required to find and graph the equation relating W, the amount of water in the pond, and T, the number of minutes.
Since water is added into the pond at a constant rate, it follows that the equation must be the equation of a line:
\(W=mT+c\)Where m is the rate at which water is added in liters per minute, and c is the amount of water in liters already in the pond.
Hence, substitute m=30 and c=600 into the equation:
\(W=30T+600\)To graph the equation, find two points (T, W) that satisfy the equation.
Substitute T=0 into the equation:
\(\begin{gathered} W=30(0)+600 \\ \Rightarrow W=0+600 \\ \Rightarrow W=600 \end{gathered}\)Hence, one point is (0,600).
Substitute T=1 to find another point:
\(W=30(1)+600=30+600=630\)Another point is (1,600).
Graph these points and join them with a straight line:
The required equation is W=30T+600.
The graph is shown above.
Related Questions
seven times a number, increased by 4
Answers
Answer:
7x+4
Step-by-step explanation:
Answer:7 times a number increased by 4 times the number
Let a number and the number be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
7 times a number: 7x
4 times the number: 4x
The phrase increased by means we add 4x to 7x:
7x + 4x
Simplifying, we get: (7 + 4)x
11x
Step-by-step explanation:
A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that less than three take the discount (round answers to three decimal places, for example, 0.xxx)
Answers
Answer:
0.551
Step-by-step explanation:
Let no. of people who take discount = x
Using binomial distribution, N c X. p^x. q^(n-x)
p : customer getting discount = 0.3, q : customer not getting discount = 0.7 n : no. of customers = 8
Probability that x < 3 : Prob (x=0) + Prob (x=1) + Prob (x=2)
= 8 c 0. (0.3)^0 . (0.7)^8 + 8 c 1. (0.3)^1 . (0.7)^7 + 8 c 2. (0.3)^2 . (0.7)^6
0.05764801 + 0.19765032 + 0.29647548
0.551
what is the negation of the statement "all summer days are muggy"
Answers
Answer:
What is the negation of the statement?
In Mathematics, the negation of a statement is the opposite of the given mathematical statement. If “P” is a statement, then the negation of statement P is represented by ~P. The symbols used to represent the negation of a statement are “~” or “¬”.
Step-by-step explanation:
Suta purrachina za waurdo
What’s the answer for this ? 1-2 question
Answers
Answer:
Question 1:
A) Parallelogram
B) Right Angled Triangle
Question 2:
Using parallelogram to use properties of parallel lines. To find whether a quadrilateral is parallelogram, first we will write it's coordinates. After writing coordinates, we find slope of each line by slope formula. After this , we compare the slope of equal lines through which we come to know whether they are parallel to eachother or not. After that, if two pairs of lines are parallel, then the given quadrilateral is a parallelogram.
right angled tri
500 - 20x ≥ 200 I need help
Answers
Answer:
x \(\leq\) 15
Step-by-step explanation:
The expression 19.95+0.20x models the daily cost of renting a car. In the expression, x represents the number of miles the car is driven. Find the cost of renting a car for a day when the car is driven 50 miles.
Answers
The cost of renting a car for a day when the car is driven 50 miles
will be;
⇒ $29.95
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 19.95 + 0.20x
Which models the daily cost of renting a car.
Where, x is represents the number of miles the car is driven.
Now,
Since, The expression is,
= 19.95 + 0.20x
Where, x is represents the number of miles the car is driven.
Hence, The cost of renting a car for a day when the car is driven 50 miles will be;
Substitute x = 50 in above equation as;
The cost of renting a car = 19.95 + 0.20 × 50
= 19.95 + 10
= $29.95
Therefore, The cost of renting a car for a day when the car is driven 50 miles will be;
⇒ $29.95
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Ticket sales for Six Flags White Water totaled $94,520 this summer. Tickets for the water park cost $17 each. How many tickets were sold?
Answers
The number of tickets that will be sold is 5560.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Ticket sales for Six Flags White Water totaled $94,520 this summer.
Tickets for the water park cost $17 each.
The number of tickets sold will be = 94520/17 = 5560.
Hence, the number of tickets that will be sold is 5560.
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SOLVE THE SYSTEM ALGEBRAICALLY
Answers
Answer: (4,3) and (-1,8)
Step-by-step explanation:
Before I solve the system, I am going to rewrite it to make it easier for me to understand it.
\(y=x^2-4x+3\\y=-x+7\)
Notice that f(x) and g(x) have been changed into y. The reason is because f(x) and g(x) are the same and stand for y, but we only use f and g to distinguish between the 2 equations. We can use equal values to solve.
\(x^2-4x+3=-x+7\) [add both sides by x]
\(x^2-3x+3=7\) [subtract both sides by 7]
\(x^2-3x-4=0\) [factor]
\((x-4)(x+1)=0\)
Notice that x-4=0 and x+1=0. This means the solutions are x=4 and x=-1.
To find the actual full solution, we have to plug those points back into the original equations.
\(-(4)+7=-4+7=3\\-(-1)+7=1+7=8\)
Therefore, the solutions to this system are (4,3) and (-1,8).
A circle has a diameter of 41 centimeters Which equation can be used to find the radius of this circle? 41 T= 2(41) T417
Answers
Answer:
If we are given diameter and we need to find radius then,
Radius(r) = Diameter(d) ÷ 2
⇒ r = d÷2
So here d = 41
So r = d÷2
⇒ r = 41 ÷ 2
⇒ r = 20.5
HELP PLEASE!!! I need to name each angle
Answers
Answer:
XWZ and ZWX are the only ways to label this angle
Step-by-step explanation:
Alexa has saved
2/7
of the cost of her trip to the Caribbean. Estimate how much money she
has left to save.
A.3/4 of the cost
B.1/2 of the cost
C.1 1/4 of the cost
D.1/4 of the cost
Answers
Answer:
A 3/4
Step-by-step explanation:
Set up equation to find the percentage 2/7 equals:
Variable x = percentage
2/7 = x/100
Cross multiply:
2 × 100 = 7 × x
200 = 7x
Divide:
28.57142... = x
About 30% (I rounded to 30% because it is a nice number to use when all other numbers end in 5 or 0)
If Alexa has about 30% saved, she will need to save about 70% more. Find the solution that is closest to 70%.
A is 3/4 which comes out to 75%. So far, this sounds like the best answer. Let's check the others just in case.
B is 1/2, or 50% which isn't as close as A was to 70%.
C is 1 1/4 which means 125% needs to be saved. This would mean Alexa is in debt and hasn't saved any money which is not the case.
D is 1/4, or 25%. The trick here is that she's saved about 30% so 25% is closest, but we are looking for how much more she needs to save.
I also need to know the value of T
Answers
Answer:
hello
Step-by-step explanation:
\(137 = - 151 + t \\ 137 + 151 = t \\ t = 288\)
hope this is correct.
16) Solve for side AB.
AB-
Round your answer to the nearest hundredth.
A) 5.45
B) 6.45
C) 7.45
Answers
Answer:
AB= 7.45
Anwer C)
Step-by-step explanation:
Cos (angle) = Nearest side / Huypothenuse
Cos(20) = 7 / AB
Cos(20) * AB = (7 /AB) * AB
Cos (20) * AB = 7
(Cos(20) *AB) / Cos(20) = 7 / Cos(20)
AB = 7 / cos(20)
AB= 7.45
In order to find the hypotenuse, we can use the trigonometric function “cosine”,
since.
Cosine =
Adjacent side (which is 7) / hypotenuse
Cos(50) = 7 / AB
AB = 7 / Cos(50)
AB = 10.89006678802289
AB ≈ 10.89
Have a good day ^^
HELP ASAP PLS ANSWER THE QUESTION IN THE PIC I GIV BRAINLEST AND LOTS OF POINTS TO CORRECT ANSWER
Answers
Answer:
ABE is the answer hope this helps
The graph shows the relationship between time and the distance a train travels.
What is the slope of the line?
?
Distance (mi)
200
150
100
50
0
ہے
Time (h)
3
Answers
Answer:
50
Step-by-step explanation:
i got it correct on the iready quiz
The graph of the line does not change except only in the y - intercept. The slope of the line remains same.
What is the general equation of the straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line is -y = mx + c
[m] : slope of line.
[c] : y - intercept
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is a graph that shows the relationship between time and the distance a train travels.
From the graph, we can write the coordinates as -
(1, 60) and (2, 120)
So, we can write the slope of the line as -
m = (120 - 60)/(2 - 1)
m = 60/1
m = 60
Therefore, the slope of the line given in the graph will be 60 miles/hr.
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What is the slope of the line?
Pls help
Answers
Answer: 3
Step-by-step explanation:
Pick 2 coordinates that are on the line, for example, (-2,0) and (-1,3)
Slope = Rise/Run = (3-0)/(-1-(-2)) = 3
A camp counselor needs 12 bags of candy that each weigh 112 pounds. How many ounces of candy does the camp counselor need?
Answers
GIVING BRAINLIEST!
PLEASE HELP!
Answers
Answer:
x < 2 is the answer oh and do the 3rd line option
The table represents a linear equation.
Which equation correctly uses point (-2, -6) to write the
equation of this line in point-slope form?
х
-4
-2
6
10
y
-11
-6
14
24
y-6 = {(x - 2)
• y-6 = (x - 2)
y +6 = } (x + 2)
y+6= {(x + 2)
Answers
Answer:
see below
Step-by-step explanation:
Considering the last two table entries, we can find the slope of the line to be ...
Δy/Δx = (24 -14)/(10 -6) = 10/4 = 5/2
The point-slope form of the equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
For (h, k) = (-2, -6) and m = 5/2, this is ...
y -(-6) = 5/2(x -(-2))
y +6 = 5/2(x +2) . . . . . matches the last choice
Answer:
d is the right choice
Step-by-step explanation:
8. The first three terms of a geometric sequence are ( x-6), 3x, and y. If the common ratio is 6, then the value of y is.
Answers
Answer:
The value of y is 216
(and the value of x is 12)
Step-by-step explanation:
The general formula for a geometric sequence is,
\(a_n = a_1(r)^{n-1}\)
Where n represents the nth term, a_1 is the first term and r is the common ratio,
we see that,
r = 6,
the first term is,
a_1 = (x-6)
the 2nd term is,
a_2 = 3x,
the 3rd term is,
a_3 = y, finding y,
first we find x, using the above given formula we have,
\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)
x = 12,
Now, for y we can use the relation between a_3 and a_2,
\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)
y = 216
GUYS! PLEASE HELP ME IN NO. 8 AND 9 WITH SOLUTIONS.
Find the area of each shaded region. Assume that all angles that appear to be right angles are right angles.
Answers
Step-by-step explanation:
Triangle
\( \frac{10 \times 4}{2} - \frac{5 \times 3}{2} = \\ = \frac{40}{2} - \frac{15}{2} = \\ = \frac{25}{2} \)
Circle
\( {4}^{2} \pi - {2}^{2} \pi = \\ = 16\pi - 4\pi = \\ = 12\pi\)
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in
20.4 days
22.5 days
25.6 days
30.1 days
Answers
Let's assume that B can do the job alone in x days.
Then, according to the question, A can do the same job alone in (1/3)x days.
Also, we know that A takes 60 days less than B to finish the job, so:
(1/3)x = x - 60
Solving for x, we get:
x = 90
Therefore, B can do the job alone in 90 days and A can do the same job alone in (1/3) * 90 = 30 days.
To find out how long they take to finish the job together, we use the formula:
(AB)/ (A+B)
where AB is the product of their individual times and A+B is their combined time.
Plugging in the values, we get:
(30 * 90)/(30+90) = 22.5
Therefore, working together, they can finish the job in 22.5 days.
Answer: Option B - 22.5 days
Mindy has already saved $20 and plans to save $8 each month.Georgette has no money saved yet but plans to to save $5 each month.Will the girls ever have saved the same amount?
Answers
Answer:
no
Step-by-step explanation:
because mindy has already saved $20 and is putting $8 which is more than the amount georgette is putting (monthly) and plus georgette has no money saved so basically mindy will have more money saved
For each of the following relations, i) state whether the relation is an equivalence relation and ii) if it is an equivalence relation, list the blocks of its corresponding partition, and if it is not, list all of the properties (reflexive, symmetric, transitive) it violates. In all cases, the relations are on the set A = {1, 2, 3, 4}
a. {(1, 1), (1,4), (2, 2), (3, 3), (4, 1), (4, 4)}
b. A x A
c. {(1, 1), (2, 2), (3, 1), (1, 3), (4, 4)
d. ({2, 3} x A) U ((1, 1), (4, 4)}
Answers
a. The relation is an equivalence relation, and its corresponding partition has blocks {1, 4}, {2}, and {3}.
b. The relation is not specified.
c. The relation is not an equivalence relation because it is not transitive.
d. The relation is not an equivalence relation because it is not reflexive.
a. The relation is an equivalence relation because it is reflexive, symmetric, and transitive. The blocks of its corresponding partition are {1, 4} and {2} and {3}.
b. The relation is not specified, so it is impossible to determine whether it is an equivalence relation or not.
c. The relation is not an equivalence relation because it is not transitive. Specifically, (3, 1) and (1, 3) are in the relation, but (3, 3) is not.
d. The relation is not an equivalence relation because it is not reflexive (i.e., 1 and 4 are not related to themselves).
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In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
Determine the value of `w(25)`.
What does this value say about the wolf population?
Answers
Answer:
w(25) = 96
There are 96 wolves in the year 2020
Step-by-step explanation:
Given:
\(w(x)=14\cdot 1.08^{x}\)
w(25) =
\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)
Number of years : 1995 + 25 = 2020
In 2020, there are 96 wolves
What is the diameter of a sphere with a volume of 18174 ft^3 to the nearest tenth of a foot?
Answers
Answer:
Diameter = 33 feet
Step-by-step explanation:
Diameter = 2 x radius
Given that the volume = 18174 \(ft^{3}\), then;
Volume of sphere = \(\frac{4}{3}\)\(\pi\)\(r^{3}\)
where r is the radius of the sphere.
Thus,
18174 = \(\frac{4}{3}\) x \(\frac{22}{7}\) x \(r^{3}\)
= \(\frac{88}{21}\) \(r^{3}\)
18174 x 21 = 88 \(r^{3}\)
381654 = 88 \(r^{3}\)
\(r^{3}\) = \(\frac{381654}{88}\)
= 4336.9773
r = \(\sqrt[3]{4336.9773}\)
r = 16.3078
The diameter of the sphere = 2 x 16.3078
= 32.6156
= 33 feet
How do I simplify this expression?
Answers
Answer:
what expression nothing shows up
Step-by-step explanation:
Answer:
plzz keep the complete question
Step-by-step explanation:
i hope u will
if it is given that "x" is 23.5 - proof that it is a point of intersection at y= 1/2(x) - 25 if y is equal to 11. been trying but not working out.
Answers
When substituting y = 11 into the equation y = 1/2(x) - 25, we find that x = 72, confirming that (23.5, 11) is a valid point of intersection.
Given that x is 23.5, it is required to prove that it is an intersection point for the equation y = 1/2(x) - 25 when y is equal to 11.
The equation is given as y = 1/2(x) - 25
When y = 11, we can substitute the value of y in the equation to obtain 11 = 1/2(x) - 25
This can be simplified as 11 + 25 = 1/2(x)36 = 1/2(x)
On solving, x = 72Thus, when y is equal to 11 and x is equal to 72, the given point of intersection is valid.
Therefore, it can be concluded that x = 23.5 is a point of intersection for the equation y = 1/2(x) - 25 when y is equal to 11.
In summary, when given an equation with two variables, we can find the point of intersection by setting one of the variables to a given value and solving for the other variable. In this case, when y is equal to 11, we can solve for x and obtain the point of intersection as (72,11).
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Draw the net and calculate the surface area .
Answers
Hello!
surface area
= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)
= 160cm²
Kiera makes 181.5 ounces of punch for a pool party. She has 5 guests attending the pool party. How many ounces of punch does she make for each guest?